Problem:
Let , and for integers , let . If is the largest value of for which the domain of is nonempty, the domain of is . What is ?
Answer Choices:
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Solution:
Because is defined if and only if , so the domain of is the interval . Similarly, the\
domain of is the solution set of the inequality , which is the interval , and the domain of is the solution set of the inequality , which is . The domain of is the solution set of the equation , which is , and because the equation has no real solutions, the domain of is empty. Therefore .
The problems on this page are the property of the MAA's American Mathematics Competitions